The width will be a much bigger problem than the height. You can always shoot your subjects seated, and lights don't need to be particularly high for most purposes (unless you're really getting dramatic). Anything centred above eye level will usually work out okay. You can even knock down the ceiling reflections pretty satisfactorily using black paint (or black-painted tiles, black fabric, etc.) if you need something more directional than the room itself provides, or if you want to restrict how much the key light influences the background. You might not have room for booms or anything of that nature, but you can fire a small gridded strobe over the backdrop (assuming you're using a fabric or paper backdrop) — you only need a couple of inches of clearance for something like that — and you can get effective hair/rim lighting, given that you have some front-to-back distance to work with.

The problem is that in order to get any real shape/modelling and you're not shooting a single person who can stand Paramount (butterfly) lighting, you'll need to get the key light off to the side. You can manage it well enough for a single subject, or even a couple who don't mind each other very much at all, but for any larger grouping, there's going to be a distinct difference in the direction and intensity of the light. The only cure for that, unfortunately, is more space (or fewer people).

As long as you are aware of the limitations, you can do a lot in a small space. At the same time, you'll quickly get to know exactly what you would do with any extra space if you had it.

Taking things outdoors when necessary is one idea, but that has its own problems. Weather will be hit-and-miss (more misses than hits if your luck is like mine), and even at the best of times, lighting and so forth are going to require a lot of help staying put. Working with on-camera flash, handheld reflectors and ambient lighting is pretty much the lot of the solo photographer, but if you have anyone who can assist (or better yet, a small army of assistants) you can work with more complex lighting setups.

Another idea would be to look into renting an occasional space/studio. There must be a local venue people rent for celebrations, yoga/meditation classes, that sort of thing, where you're not committing to any long-term real estate deals. It can make sense to rent a larger space for, say, one day or one weekend per month (or even less frequently). Line up a number of clients for that time, then shoot them all while you have the space. It'll be horribly expensive (likely) compared to full-time rental, but it will get you work and referrals you wouldn't be able to get otherwise. If there's enough business to make occasional rental a real chore, there's probably enough business to support a "real" studio of your own.